Question: Simplify the following expression: $a = \dfrac{5z^2 + 30z - 80}{z + 8} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ a =\dfrac{5(z^2 + 6z - 16)}{z + 8} $ Then we factor the remaining polynomial: $z^2 + {6}z {-16} $ ${8} {-2} = {6}$ ${8} \times {-2} = {-16}$ $ (z + {8}) (z {-2}) $ This gives us a factored expression: $\dfrac{5(z + {8}) (z {-2})}{z + 8}$ We can divide the numerator and denominator by $(z - 8)$ on condition that $z \neq -8$ Therefore $a = 5(z - 2); z \neq -8$